The industrial internet of things allows manufacturers to acquire large amounts of data. This opportunity, assuming the right methods are available, allows manufacturers to find anomalies that arise during manufacturing system operation. Data acquired from a manufacturing system are usually in the forms of time series. This paper proposes a new method that can detect anomalies in time series data. This model is based on recurrent neural networks, and it can be trained using data acquired during routine system operation. This is very beneficial because often, there are few data labeled as anomalies, since anomalies are hopefully rare events in a well-managed manufacturing system. The model takes time series data as an input and reconstructs the input data. Time series data with an anomaly would causes patterns in the reconstruction errors that are inconsistent with error patterns of anomaly-free data. The performance of the proposed method is assessed using data from a diesel engine assembly process. Three common types of anomalies are detected from the time series data. It is shown that the method not only can detect anomalies, but it can also provide insights into the timestep at which the anomaly occurred. This feature helps a manufacturer pinpoint the source of the problem.